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I see a lot of questions like:

What is the next term in the sequence 20,5,3,6,7,12, ... ?

I think they are asked daily. They are generally closed, but can't we do anything to reduce the number of questions asked in this manner? Furthermore, I think it would be good to point out that the question can be asked on Puzzling. SE.

I see three solutions:

  1. Adding a note to the tag excerpt that questions that ask for the next term in the sequence are off-topic and can be asked on Puzzling.SE.

    Problem: People who have a mathematical question about finding the next term in an arithmetic, geometric or harmonic progression might think that the question is off-topic.

  2. Perhaps better than the first one: Note in the excerpt that it is for sequences and series related to calculus. Although I'm not sure that is the only thing the tag should be used for.

  3. Adding a migration path to Puzzling.SE, so that question can be migrated there more easily.

    Problem: Puzzling.SE is currently in beta, so I'm not sure if it is even allowed.

Please discuss whether we should do anything about this.

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    $\begingroup$ It is worth mentioning that there were several posts about this type of questions in the past, see for example here or here. $\endgroup$ – Martin Sleziak Jul 26 '15 at 10:28
  • $\begingroup$ The tag-info for pattern-recognition has a few paragraphs mentioning that without sufficient context, such questions will probably be closed. $\endgroup$ – Martin Sleziak Jul 26 '15 at 10:31
  • $\begingroup$ As explained in comments here (and probably in several other posts), it is not possible to add migration path to puzzling.SE is very unlikely at the moment, since it is still beta. $\endgroup$ – Martin Sleziak Jul 26 '15 at 11:43
  • $\begingroup$ @MartinSleziak Can you clarify the third comment? Is it not possible or very unlikely? $\endgroup$ – wythagoras Jul 26 '15 at 11:47
  • $\begingroup$ wythagoras: Maybe this answer could clarify what the position on migration paths to beta sites is. $\endgroup$ – Martin Sleziak Jul 26 '15 at 11:49
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    $\begingroup$ IMHO, this sort of questions should be closed as off-topic because of missing context. Without extra context, this sort of question usually admit infinitely many solutions. $\endgroup$ – achille hui Jul 26 '15 at 13:27
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    $\begingroup$ Migrating to puzzling.SE is probably not a good idea, since some questions of this sort appear to be closed as too broad. See for example this question. $\endgroup$ – Daniel R Jul 26 '15 at 15:30
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    $\begingroup$ And the people of puzzling.SE think this sort of question belongs here... People need to understand mutually what is and isn't on-topic before a migration path is opened. $\endgroup$ – Najib Idrissi Jul 26 '15 at 15:43
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    $\begingroup$ Finding the next term in a sequence is quite possibly the most boring "puzzle" I can imagine, to be honest. It's just not a good type of question anywhere, in general. $\endgroup$ – pjs36 Jul 26 '15 at 16:55
  • $\begingroup$ There's an outlier that actually is a decent question about conventional notation. What is the next term in the sequence "x,y,z"? $\endgroup$ – Karl Kronenfeld Aug 3 '15 at 2:46
  • $\begingroup$ Puzzling graduated. You may want to open up this discussion again, especially about the migration. $\endgroup$ – Mithrandir Sep 11 '16 at 13:14
  • $\begingroup$ @Mithrandir Well, I'm not so sure whether its a good idea to have a migration path, since it might lead to bad questions being migrated. $\endgroup$ – wythagoras Sep 11 '16 at 14:20
  • $\begingroup$ Well, then the migration ca be rejected. $\endgroup$ – Mithrandir Sep 11 '16 at 14:22
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I'd suggest closing as duplicate with a generic Q/A, which

  • makes clear that any continuation is possible
  • shows how to find continuations for simple cases (e.g., method of repeated diffferences for polynomial sequences)
  • informs how look for sequences on OEIS.org
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    $\begingroup$ This is indeed a good idea. $\endgroup$ – wythagoras Jul 28 '15 at 9:39
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    $\begingroup$ Maybe bullet 4: Show off some standard types of patterns (arithmetic progressions, geometric progressions, special sequences such as the Fibonacci sequence, ...) $\endgroup$ – AlexR Jul 28 '15 at 17:35
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The vast majority of these questions is indeed off-topic. Their closing should continue.

However, doing this with appropriate explanation (e.g. pointing to Puzzling.SE) can become tedious. On the other hand, a migration path is not going to happen as long as Puzzling is in beta, given earlier discussion about this (as linked to by Martin Sleziak). Moreover, as some commenters pointed out, Puzzling.SE isn't too happy about these questions either, so probably the migration path would incite well-meant but actually unwanted behaviour.

I also think that introducing paragraphs about off-topicness of certain questions in tag excerpts will have a very marginal effect, because people don't usually read the full tag wiki, and the tag excerpt itself is generally too valuable to waste on what something is not.

But then, it is obvious that we should try and do something about this. Perhaps a comment template can be crafted for this type of question, that can be used by those who routinely find these questions and cannot muster the motivation to accompany every close vote with a detailed explanation.

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  • $\begingroup$ What do you exactly mean by "the tag excerpt itself is generally too valuable to waste on what something is not"? If you mean in terms of characters, there are plenty of characters left in the sequences-and-series excerpt. $\endgroup$ – wythagoras Jul 26 '15 at 11:59
  • $\begingroup$ @wythagoras Because tags are already so often misused, we'd better have the small excerpt, shown when selecting tags, describe in which cases the tag is relevant, instead of describing in which cases it's not. An exception to this is pointing to another tag, but since we're discussing a fragment of off-topic questions here, that doesn't really apply. $\endgroup$ – Lord_Farin Jul 26 '15 at 12:01
  • $\begingroup$ @Lord_Farin If you mean (sequences-and-series), it might be only a small fraction, but I'd guess that most questions in (pattern-recognition) are of this type. $\endgroup$ – Martin Sleziak Jul 26 '15 at 12:15
  • $\begingroup$ @Martin You're probably right. But then my first thought is that maybe a more fundamental discussion about pattern-recognition is in order. $\endgroup$ – Lord_Farin Jul 26 '15 at 12:17
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As a slight variation on this answer, I propose a canonical question explaining why such questions are ambiguous, which can be linked to from such questions to help the OP understand the issue. This canonical question should be linked here to be discoverable. I wrote this candidate Q/A.

Reasoning

As others have pointed out, in many specific cases it is possible to provide a useful answer (eg if one extrapolation is widely agreed to be most natural, and most likely to be the OP's intention), so marking as duplicate is not always appropriate.

Consider this specific example. First note that an answer was given which is very likely consistent with the OP's intention. Secondly note the following comment which attempts to point out the inherent ambiguity:

Declare that the full sequence is $$19,25,45,87,159,0,0,0,0,0,\ldots$$ and you can write down a simple formula involving Iverson brackets or Kronecker deltas.

Based on the OP's response, I don't think it worked:

The full sequence is 19, 25, 45, 87, 159, 269, 425, 635, 907, 1249, 1669, 2175, 2775, 3477, 4289, 5219.

I think a comment linking to a well-written explanation of the issue would have been more effective.

(btw I don't know what the etiquette is for zombie discussions on math.meta, and there's no math.meta.meta to ask on :))

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Suppose it really is a mathematical question, not a puzzle. If they haven't done their own work (such as checking OEIS), then put it on hold.

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    $\begingroup$ "I checked the OEIS and it was not listed" might make the question less likely to be closed. On the flip side, "translated" sequences (e.g. shifted by a constant) won't show up, and a non-savvy user might not think to do an appropriate shift. $\endgroup$ – J. M. is a poor mathematician Jul 29 '15 at 13:51

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